Reading about Husserl at the hairdresser

I've been trying to understand where Husserl is coming from, because until I've done that I'll find it difficult to explain how Heidegger and the existentialists differ. Even Husserl's transcendental philosophy is not as clear cut as I thought it was, having so far only really read research papers that skate in a fairly perfunctory way over the philosophical distinctions between Husserl and Heidegger.

Well, I'm working my way through Dan Zahavi's book "Husserl's Phenomenology" for which I have high hopes that it will reveal to me in plain English what so far has proved elusive: what are the ideas of Husserl's phenomenology based on, and why is bracketing as a technique applied in the epoche thought to be so fundamental to discovering the essence of an experience?

While I was at the hairdresser, I pulled out the book and resumed my place in the chapter covering Husserl's turn to transcendental philosophy. According to Zahavi, Husserl himself pointed out that "it is quite a puzzle how consciousness can be something absolute that constitutes all transcendence, including the entire psycho-physical world, and simultaneously as something that appears as a real part of the world" (p48) There is a distinction made between psychological reflection and transcendental reflection. The former is a kind of mundane self-consciousness in which one interprets an act as a psychical process occurring in the world, whereas the latter is not immediately available to us in our everyday thoughts. Transcendental reflection involves stripping a subjective awareness of its contingent interpretations. Basically, this is the process that is carried out in the epoche for the reduction to get to the essence of a phenomenon.

This still doesn't make complete sense to me, but there is much more to read yet.